Question

A ray of light falls normally on a refracting face of a prism of refractive index is 1.5.Then the angle of prism if the ray just fails to emerge from the second refracting surface is

Answer 1

In this case critical angle is equal to angle of prism.
sinA=sinC=1/1.5

Answer 2

The angle of prism when ray fails to emerge from the second refracting surface is 48°

The first face of the prism will be i1 = 0 and sin 0 =0  

According to the Snell’s law

sin i1 = 1.5 and sin r1  = 0  

Similarly, for a prism - r1 + r2 = A  

= 0 + r2 = A

= r2 = A --- eq 1

The second face of the prism will fail to emerge, thus -

= r2 = θc --- eq 2

= A = r2 = θc  

θc = sin-1(1/μ)

θc = sin-1(1/1.5) = sin-1 (2/3) = 42º

A = 42º

δ = i1 + i2 – A

= 0 + 90 -42

= 48º

Therefore, the angle of the prism is 48°